91Ó°ÊÓ

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope \(m\). Sketch the line. \((-2,-5), \quad m \equiv \frac{3}{4}\)

Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values. $$ f(x)=3 x^{2}-2 x-5 $$

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts. $$ y=\frac{2}{3} x-1 $$

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope \(m\). Sketch the line. \((6,-1), \quad m\) is undefined.

Write an equation for the function that is described by the given characteristics. The shape of \(f(x)=|x|\), but shifted 12 units upward and reflected in the \(x\) -axis

Write a sentence using the variation terminology of this section to describe the formula. Area of a triangle: \(A=\frac{1}{2} b h\)

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts. $$ y=x^{2}-4 x+3 $$

(a) find the inverse function of \(f\), (b) graph both \(f\) and \(f^{-1}\) on the same set of coordinate axes, (c) describe the relationship between the graphs of \(f\) and \(f^{-1}\), and (d) state the domain and range of \(f\) and \(f^{-1}\). $$ f(x)=\sqrt[3]{x-1} $$

Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values. $$ f(x)=-x^{2}+3 x-2 $$

Find all real values of \(x\) such that \(f(x)=0\). $$ f(x)=15-3 x $$